Daily Papers

LLMs have emerged as powerful tools for interpreting multimodal data. In medicine, they hold particular promise for synthesizing large volumes of clinical information into actionable insights and digital health applications. Yet, a major limitation remains their inability to handle time series. To overcome this gap, we present OpenTSLM, a family of Time Series Language Models (TSLMs) created by integrating time series as a native modality to pretrained LLMs, enabling reasoning over multiple time series of any length. We investigate two architectures for OpenTSLM. The first, OpenTSLM-SoftPrompt, models time series implicitly by concatenating learnable time series tokens with text tokens via soft prompting. Although parameter-efficient, we hypothesize that explicit time series modeling scales better and outperforms implicit approaches. We thus introduce OpenTSLM-Flamingo, which integrates time series with text via cross-attention. We benchmark both variants against baselines that treat time series as text tokens or plots, across a suite of text-time-series Chain-of-Thought (CoT) reasoning tasks. We introduce three datasets: HAR-CoT, Sleep-CoT, and ECG-QA-CoT. Across all, OpenTSLM models outperform baselines, reaching 69.9 F1 in sleep staging and 65.4 in HAR, compared to 9.05 and 52.2 for finetuned text-only models. Notably, even 1B-parameter OpenTSLM models surpass GPT-4o (15.47 and 2.95). OpenTSLM-Flamingo matches OpenTSLM-SoftPrompt in performance and outperforms on longer sequences, while maintaining stable memory requirements. By contrast, SoftPrompt grows exponentially in memory with sequence length, requiring around 110 GB compared to 40 GB VRAM when training on ECG-QA with LLaMA-3B. Expert reviews by clinicians find strong reasoning capabilities exhibited by OpenTSLMs on ECG-QA. To facilitate further research, we provide all code, datasets, and models open-source.

Time series models face significant challenges in scaling to handle large and complex datasets, akin to the scaling achieved by large language models (LLMs). The unique characteristics of time series data and the computational demands of model scaling necessitate innovative approaches. While researchers have explored various architectures such as Transformers, LSTMs, and GRUs to address these challenges, we propose a novel solution using RWKV-7, which incorporates meta-learning into its state update mechanism. By integrating RWKV-7's time mix and channel mix components into the transformer-based time series model Timer, we achieve a substantial performance improvement of approximately 1.13 to 43.3x and a 4.5x reduction in training time with 1/23 parameters, all while utilizing fewer parameters. Our code and model weights are publicly available for further research and development at https://github.com/Alic-Li/BlackGoose_Rimer.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Time series, characterized by a sequence of data points organized in a discrete-time order, are ubiquitous in real-world scenarios. Unlike other data modalities, time series present unique challenges due to their intricate and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing such data is of great significance in practical applications and has been extensively studied for centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to contemporary deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks. TSLib implements 30 prominent models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 13 advanced deep time series models across diverse tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, providing insights for research and adoption of deep time series models. Code and datasets are available at https://github.com/thuml/Time-Series-Library.

Traditional saliency map methods, popularized in computer vision, highlight individual points (pixels) of the input that contribute the most to the model's output. However, in time-series they offer limited insights as semantically meaningful features are often found in other domains. We introduce Cross-domain Integrated Gradients, a generalization of Integrated Gradients. Our method enables feature attributions on any domain that can be formulated as an invertible, differentiable transformation of the time domain. Crucially, our derivation extends the original Integrated Gradients into the complex domain, enabling frequency-based attributions. We provide the necessary theoretical guarantees, namely, path independence and completeness. Our approach reveals interpretable, problem-specific attributions that time-domain methods cannot capture, on three real-world tasks: wearable sensor heart rate extraction, electroencephalography-based seizure detection, and zero-shot time-series forecasting. We release an open-source Tensorflow/PyTorch library to enable plug-and-play cross-domain explainability for time-series models. These results demonstrate the ability of cross-domain integrated gradients to provide semantically meaningful insights in time-series models that are impossible with traditional time-domain saliency.

We introduce the Cisco Time Series Model, a univariate zero-shot forecaster. This time series foundation model is the result of a general architectural innovation to a time series model enabling it to accept multiresolution input, applied to a popular decoder-only time series model (TimesFM). The resulting multiresolution decoder-only model is trained on over 300B unique data points, with more than half coming from the observability domain. Quantitative and qualitative evaluations demonstrate that the resulting model achieves superior performance on observability datasets while retaining very similar performance on a standard general-purpose forecasting benchmark (GIFT-Eval), and suggest that the multiresolution structure enables the model to make more accurate predictions on long context input.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series. We present TimeX, a time series consistency model for training explainers. TimeX trains an interpretable surrogate to mimic the behavior of a pretrained time series model. It addresses the issue of model faithfulness by introducing model behavior consistency, a novel formulation that preserves relations in the latent space induced by the pretrained model with relations in the latent space induced by TimeX. TimeX provides discrete attribution maps and, unlike existing interpretability methods, it learns a latent space of explanations that can be used in various ways, such as to provide landmarks to visually aggregate similar explanations and easily recognize temporal patterns. We evaluate TimeX on eight synthetic and real-world datasets and compare its performance against state-of-the-art interpretability methods. We also conduct case studies using physiological time series. Quantitative evaluations demonstrate that TimeX achieves the highest or second-highest performance in every metric compared to baselines across all datasets. Through case studies, we show that the novel components of TimeX show potential for training faithful, interpretable models that capture the behavior of pretrained time series models.

For a long-time, researchers have been developing a reliable and accurate predictive model for stock price prediction. According to the literature, if predictive models are correctly designed and refined, they can painstakingly and faithfully estimate future stock values. This paper demonstrates a set of time series, econometric, and various learning-based models for stock price prediction. The data of Infosys, ICICI, and SUN PHARMA from the period of January 2004 to December 2019 was used here for training and testing the models to know which model performs best in which sector. One time series model (Holt-Winters Exponential Smoothing), one econometric model (ARIMA), two machine Learning models (Random Forest and MARS), and two deep learning-based models (simple RNN and LSTM) have been included in this paper. MARS has been proved to be the best performing machine learning model, while LSTM has proved to be the best performing deep learning model. But overall, for all three sectors - IT (on Infosys data), Banking (on ICICI data), and Health (on SUN PHARMA data), MARS has proved to be the best performing model in sales forecasting.

The industry is rich in cases when we are required to make forecasting for large amounts of time series at once. However, we might be in a situation where we can not afford to train a separate model for each of them. Such issue in time series modeling remains without due attention. The remedy for this setting is the establishment of a foundation model. Such a model is expected to work in zero-shot and few-shot regimes. However, what should we take as a training dataset for such kind of model? Witnessing the benefits from the enrichment of NLP datasets with artificially-generated data, we might want to adopt their experience for time series. In contrast to natural language, the process of generation of synthetic time series data is even more favorable because it provides full control of series patterns, time horizons, and number of samples. In this work, we consider the essential question if it is advantageous to train a foundation model on synthetic data or it is better to utilize only a limited number of real-life examples. Our experiments are conducted only for regular time series and speak in favor of leveraging solely the real time series. Moreover, the choice of the proper source dataset strongly influences the performance during inference. When provided access even to a limited quantity of short time series data, employing it within a supervised framework yields more favorable results than training on a larger volume of synthetic data. The code for our experiments is publicly available on Github https://github.com/sb-ai-lab/synthesize_or_not.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Stock selection, which aims to predict stock prices and identify the most profitable ones, is a crucial task in finance. While existing methods primarily focus on developing model structures and building graphs for improved selection, pre-training strategies remain underexplored in this domain. Current stock series pre-training follows methods from other areas without adapting to the unique characteristics of financial data, particularly overlooking stock-specific contextual information and the non-stationary nature of stock prices. Consequently, the latent statistical features inherent in stock data are underutilized. In this paper, we propose three novel pre-training tasks tailored to stock data characteristics: stock code classification, stock sector classification, and moving average prediction. We develop the Stock Specialized Pre-trained Transformer (SSPT) based on a two-layer transformer architecture. Extensive experimental results validate the effectiveness of our pre-training methods and provide detailed guidance on their application. Evaluations on five stock datasets, including four markets and two time periods, demonstrate that SSPT consistently outperforms the market and existing methods in terms of both cumulative investment return ratio and Sharpe ratio. Additionally, our experiments on simulated data investigate the underlying mechanisms of our methods, providing insights into understanding price series. Our code is publicly available at: https://github.com/astudentuser/Pre-training-Time-Series-Models-with-Stock-Data-Customization.

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

A unified foundation model for medical time series -- pretrained on open access and ethics board-approved medical corpora -- offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments. However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 10% and 7% in out-of-distribution and in-distribution scenarios, respectively, when compared to other zero-shot and fine-tuned baselines. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

Inspired by recent advancements in large language models (LLMs) for Natural Language Processing (NLP), there has been a surge in research focused on developing foundational models for time series forecasting. One approach involves training LLM architectures on tokenized time series data using cross-entropy loss. Although this method has demonstrated promising results, cross-entropy loss is primarily designed for classification tasks and does not account for the distance between classes. To address this limitation, we propose using the Wasserstein loss for such architectures. To validate our approach, we fine-tuned a foundational time series model on 22 zero-shot datasets, comparing the performance of cross-entropy loss with that of Wasserstein loss. Our results demonstrate that replacing cross-entropy loss with Wasserstein loss significantly improves point estimation.

The reliability of deep time series models is often compromised by their tendency to rely on confounding factors, which may lead to misleading results. Our newly recorded, naturally confounded dataset named P2S from a real mechanical production line emphasizes this. To tackle the challenging problem of mitigating confounders in time series data, we introduce Right on Time (RioT). Our method enables interactions with model explanations across both the time and frequency domain. Feedback on explanations in both domains is then used to constrain the model, steering it away from the annotated confounding factors. The dual-domain interaction strategy is crucial for effectively addressing confounders in time series datasets. We empirically demonstrate that RioT can effectively guide models away from the wrong reasons in P2S as well as popular time series classification and forecasting datasets.

By encoding time series as a string of numerical digits, we can frame time series forecasting as next-token prediction in text. Developing this approach, we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can surprisingly zero-shot extrapolate time series at a level comparable to or exceeding the performance of purpose-built time series models trained on the downstream tasks. To facilitate this performance, we propose procedures for effectively tokenizing time series data and converting discrete distributions over tokens into highly flexible densities over continuous values. We argue the success of LLMs for time series stems from their ability to naturally represent multimodal distributions, in conjunction with biases for simplicity, and repetition, which align with the salient features in many time series, such as repeated seasonal trends. We also show how LLMs can naturally handle missing data without imputation through non-numerical text, accommodate textual side information, and answer questions to help explain predictions. While we find that increasing model size generally improves performance on time series, we show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers, and poor uncertainty calibration, which is likely the result of alignment interventions such as RLHF.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Missing values, irregularly collected samples, and multi-resolution signals commonly occur in multivariate time series data, making predictive tasks difficult. These challenges are especially prevalent in the healthcare domain, where patients' vital signs and electronic records are collected at different frequencies and have occasionally missing information due to the imperfections in equipment or patient circumstances. Researchers have handled each of these issues differently, often handling missing data through mean value imputation and then using sequence models over the multivariate signals while ignoring the different resolution of signals. We propose a unified model named Multi-resolution Flexible Irregular Time series Network (Multi-FIT). The building block for Multi-FIT is the FIT network. The FIT network creates an informative dense representation at each time step using signal information such as last observed value, time difference since the last observed time stamp and overall mean for the signal. Vertical FIT (FIT-V) is a variant of FIT which also models the relationship between different temporal signals while creating the informative dense representations for the signal. The multi-FIT model uses multiple FIT networks for sets of signals with different resolutions, further facilitating the construction of flexible representations. Our model has three main contributions: a.) it does not impute values but rather creates informative representations to provide flexibility to the model for creating task-specific representations b.) it models the relationship between different signals in the form of support signals c.) it models different resolutions in parallel before merging them for the final prediction task. The FIT, FIT-V and Multi-FIT networks improve upon the state-of-the-art models for three predictive tasks, including the forecasting of patient survival.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Time series data is a prevalent form of data found in various fields. It consists of a series of measurements taken over time. Forecasting is a crucial application of time series models, where future values are predicted based on historical data. Accurate forecasting is essential for making well-informed decisions across industries. When it comes to electric vehicles (EVs), precise predictions play a key role in planning infrastructure development, load balancing, and energy management. This study introduces a BI-LSTM embedding denoising autoencoder model (BDM) designed to address time series problems, focusing on short-term EV charging load prediction. The performance of the proposed model is evaluated by comparing it with benchmark models like Transformer, CNN, RNN, LSTM, and GRU. Based on the results of the study, the proposed model outperforms the benchmark models in four of the five-time steps, demonstrating its effectiveness for time series forecasting. This research makes a significant contribution to enhancing time series forecasting, thereby improving decision-making processes.

Masked time series modeling has recently gained much attention as a self-supervised representation learning strategy for time series. Inspired by masked image modeling in computer vision, recent works first patchify and partially mask out time series, and then train Transformers to capture the dependencies between patches by predicting masked patches from unmasked patches. However, we argue that capturing such patch dependencies might not be an optimal strategy for time series representation learning; rather, learning to embed patches independently results in better time series representations. Specifically, we propose to use 1) the simple patch reconstruction task, which autoencode each patch without looking at other patches, and 2) the simple patch-wise MLP that embeds each patch independently. In addition, we introduce complementary contrastive learning to hierarchically capture adjacent time series information efficiently. Our proposed method improves time series forecasting and classification performance compared to state-of-the-art Transformer-based models, while it is more efficient in terms of the number of parameters and training/inference time. Code is available at this repository: https://github.com/seunghan96/pits.

The scientific reasoning ability of large language models (LLMs) has recently attracted significant attention. Time series, as a fundamental modality in scientific data, presents unique challenges that are often overlooked in current multimodal LLMs, which either encode numerical sequences as text or convert them into images. Such approaches may be insufficient for comprehensive scientific time series understanding and generation. Existing unified time series models typically specialise in either forecasting or analysis, and their effectiveness on non-periodic, heterogeneous scientific signals remains unclear. To address these gaps, we introduce SciTS, a benchmark spanning 12 scientific domains and 43 tasks, with over 50k+ instances, both univariate and multivariate signals ranging from 10^0 to 10^7 in length and up to 10~MHz in frequency. We benchmark 17 models, including text-only LLMs, multimodal LLMs, and unified time series models, and find that general-purpose LLMs exhibit stronger generalisability than specialised time series models, while representing time series as text or images limits their performance due to excessively long sequences and loss of numerical precision, respectively. We then introduce TimeOmni, a framework that equips LLMs with the ability to understand and generate time series while remaining compatible with general-purpose LLM training. This work fills a gap in both dedicated benchmarks and modelling frameworks for scientific time series, paving the way for LLMs to understand and generate complex temporal scientific data.

We present Timer-XL, a generative Transformer for unified time series forecasting. To uniformly predict 1D and 2D time series, we generalize next token prediction, predominantly adopted for causal generation of 1D sequences, to multivariate next token prediction. The proposed paradigm uniformly formulates various forecasting scenarios as a long-context generation problem. We opt for the generative Transformer, which can capture global-range and causal dependencies while providing contextual flexibility, to implement unified forecasting on univariate series characterized by non-stationarity, multivariate time series with complicated dynamics and correlations, and covariate-informed contexts that include both endogenous and exogenous variables. Technically, we propose a universal TimeAttention to facilitate generative Transformers on time series, which can effectively capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches) and is further strengthened by position embeddings in both temporal and variable dimensions. Timer-XL achieves state-of-the-art performance across challenging forecasting benchmarks through a unified approach. As a large time series model, it demonstrates notable model transferability by large-scale pre-training, as well as contextual flexibility in token lengths, positioning it as a one-for-all forecaster.

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world small-sample scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progresses have been achieved as the emergence of large language models, exhibiting unprecedented ability in few-shot generalization, scalability, and task generality, which is however absent in time series models. To change the current practices of training small models on specific datasets from scratch, this paper aims at an early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), that is pre-trained by autoregressive next token prediction on large multi-domain datasets, and is fine-tuned to downstream scenarios with promising abilities as an LTSM.

Unsupervised domain adaptation (UDA) enables the transfer of models trained on source domains to unlabeled target domains. However, transferring complex time series models presents challenges due to the dynamic temporal structure variations across domains. This leads to feature shifts in the time and frequency representations. Additionally, the label distributions of tasks in the source and target domains can differ significantly, posing difficulties in addressing label shifts and recognizing labels unique to the target domain. Effectively transferring complex time series models remains a formidable problem. We present Raincoat, the first model for both closed-set and universal domain adaptation on complex time series. Raincoat addresses feature and label shifts by considering both temporal and frequency features, aligning them across domains, and correcting for misalignments to facilitate the detection of private labels. Additionally, Raincoat improves transferability by identifying label shifts in target domains. Our experiments with 5 datasets and 13 state-of-the-art UDA methods demonstrate that Raincoat can improve transfer learning performance by up to 16.33% and can handle both closed-set and universal domain adaptation.

Text offers intuitive access to information. This can, in particular, complement the density of numerical time series, thereby allowing improved interactions with time series models to enhance accessibility and decision-making. While the creation of question-answering datasets and models has recently seen remarkable growth, most research focuses on question answering (QA) on vision and text, with time series receiving minute attention. To bridge this gap, we propose a challenging novel time series QA (TSQA) dataset, QuAnTS, for Question Answering on Time Series data. Specifically, we pose a wide variety of questions and answers about human motion in the form of tracked skeleton trajectories. We verify that the large-scale QuAnTS dataset is well-formed and comprehensive through extensive experiments. Thoroughly evaluating existing and newly proposed baselines then lays the groundwork for a deeper exploration of TSQA using QuAnTS. Additionally, we provide human performances as a key reference for gauging the practical usability of such models. We hope to encourage future research on interacting with time series models through text, enabling better decision-making and more transparent systems.

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal (cross-time) and variate (cross-variate) dependencies. While Transformer-based models have gained popularity for their flexibility in capturing both sequential and cross-variate relationships, it is unclear how to best integrate these two sources of information in the context of the Transformer architecture while optimizing for both performance and efficiency. We re-purpose the Transformer architecture to effectively model both cross-time and cross-variate dependencies. Our approach begins by embedding each variate independently into a variate-wise representation that captures its cross-time dynamics, and then models cross-variate dependencies through attention mechanisms on these learned embeddings. Gating operations in both cross-time and cross-variate modeling phases regulate information flow, allowing the model to focus on the most relevant features for accurate predictions. Our method achieves state-of-the-art performance across 13 real-world datasets and can be seamlessly integrated into other Transformer-based and LLM-based forecasters, delivering performance improvements up to 20.7\% over original models. Code is available at this repository: https://github.com/nyuolab/Gateformer.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work. Specifically, Transformers is arguably the most successful solution to extract the semantic correlations among the elements in a long sequence. However, in time series modeling, we are to extract the temporal relations in an ordered set of continuous points. While employing positional encoding and using tokens to embed sub-series in Transformers facilitate preserving some ordering information, the nature of the permutation-invariant self-attention mechanism inevitably results in temporal information loss. To validate our claim, we introduce a set of embarrassingly simple one-layer linear models named LTSF-Linear for comparison. Experimental results on nine real-life datasets show that LTSF-Linear surprisingly outperforms existing sophisticated Transformer-based LTSF models in all cases, and often by a large margin. Moreover, we conduct comprehensive empirical studies to explore the impacts of various design elements of LTSF models on their temporal relation extraction capability. We hope this surprising finding opens up new research directions for the LTSF task. We also advocate revisiting the validity of Transformer-based solutions for other time series analysis tasks (e.g., anomaly detection) in the future. Code is available at: https://github.com/cure-lab/LTSF-Linear.

In the Venture Capital(VC) industry, predicting the success of startups is challenging due to limited financial data and the need for subjective revenue forecasts. Previous methods based on time series analysis or deep learning often fall short as they fail to incorporate crucial inter-company relationships such as competition and collaboration. Regarding the issues, we propose a novel approach using GrahphRAG augmented time series model. With GraphRAG, time series predictive methods are enhanced by integrating these vital relationships into the analysis framework, allowing for a more dynamic understanding of the startup ecosystem in venture capital. Our experimental results demonstrate that our model significantly outperforms previous models in startup success predictions. To the best of our knowledge, our work is the first application work of GraphRAG.

Time series forecasting has attracted significant attention in recent decades. Previous studies have demonstrated that the Channel-Independent (CI) strategy improves forecasting performance by treating different channels individually, while it leads to poor generalization on unseen instances and ignores potentially necessary interactions between channels. Conversely, the Channel-Dependent (CD) strategy mixes all channels with even irrelevant and indiscriminate information, which, however, results in oversmoothing issues and limits forecasting accuracy. There is a lack of channel strategy that effectively balances individual channel treatment for improved forecasting performance without overlooking essential interactions between channels. Motivated by our observation of a correlation between the time series model's performance boost against channel mixing and the intrinsic similarity on a pair of channels, we developed a novel and adaptable Channel Clustering Module (CCM). CCM dynamically groups channels characterized by intrinsic similarities and leverages cluster information instead of individual channel identities, combining the best of CD and CI worlds. Extensive experiments on real-world datasets demonstrate that CCM can (1) boost the performance of CI and CD models by an average margin of 2.4% and 7.2% on long-term and short-term forecasting, respectively; (2) enable zero-shot forecasting with mainstream time series forecasting models; (3) uncover intrinsic time series patterns among channels and improve interpretability of complex time series models.

Time-series reasoning remains a significant challenge in multimodal large language models (MLLMs) due to the dynamic temporal patterns, ambiguous semantics, and lack of temporal priors. In this work, we introduce TimeMaster, a reinforcement learning (RL)-based method that enables time-series MLLMs to perform structured, interpretable reasoning directly over visualized time-series inputs and task prompts. TimeMaster adopts a three-part structured output format, reasoning, classification, and domain-specific extension, and is optimized via a composite reward function that aligns format adherence, prediction accuracy, and open-ended insight quality. The model is trained using a two-stage pipeline: we first apply supervised fine-tuning (SFT) to establish a good initialization, followed by Group Relative Policy Optimization (GRPO) at the token level to enable stable and targeted reward-driven improvement in time-series reasoning. We evaluate TimeMaster on the TimerBed benchmark across six real-world classification tasks based on Qwen2.5-VL-3B-Instruct. TimeMaster achieves state-of-the-art performance, outperforming both classical time-series models and few-shot GPT-4o by over 14.6% and 7.3% performance gain, respectively. Notably, TimeMaster goes beyond time-series classification: it also exhibits expert-like reasoning behavior, generates context-aware explanations, and delivers domain-aligned insights. Our results highlight that reward-driven RL can be a scalable and promising path toward integrating temporal understanding into time-series MLLMs.

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.

Time-series analysis is critical for a wide range of fields such as healthcare, finance, transportation, and energy, among many others. The practical applications often involve analyzing time-series data alongside contextual information in the form of natural language to support informed decisions. However, current time-series models are limited in their ability to perform reasoning that involves both time-series and their textual content. In this work, we address this gap by introducing Chat-TS, a large language model (LLM) based framework, designed to support reasoning over time series and textual data. Unlike traditional models, Chat-TS integrates time-series tokens into LLMs' vocabulary, enhancing its reasoning ability over both modalities without compromising the core natural language capabilities, enabling practical analysis and reasoning across modalities. To support learning and evaluation in this setup, we contribute new datasets: the TS Instruct Training Dataset which pairs diverse time-series data with relevant text instructions and responses for instruction tuning, the TS Instruct Question and Answer (QA) Gold Dataset which provides multiple-choice questions designed to evaluate multimodal reasoning, and a TS Instruct Quantitative Probing Set which contains a small subset of the TS Instruct QA tasks alongside math and decision-making questions for LLM evaluation. We designed a training strategy to preserve the inherent reasoning capabilities of LLMs while augmenting them for time-series reasoning. Experiments show that Chat-TS achieves state-of-the-art performance in multi-modal reasoning tasks by maintaining strong natural language proficiency while improving time-series reasoning. ~To ensure replicability and facilitate future research, all models, datasets, and code will be available at [\texttt{Github-URL].}

Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review Transformer schemes for time series modeling by highlighting their strengths as well as limitations. In particular, we examine the development of time series Transformers in two perspectives. From the perspective of network structure, we summarize the adaptations and modifications that have been made to Transformers in order to accommodate the challenges in time series analysis. From the perspective of applications, we categorize time series Transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.

Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, model weights, and data will be released.

Time series data is fundamental to decision-making in many crucial domains including healthcare, finance, and environmental science. However, analyzing this data often requires incorporating unstructured contextual information, answering domain-specific questions, and generating natural language explanations -- capabilities that traditional time series models lack due to their inability to process text. While Large Language Models (LLMs) excel at contextual reasoning and knowledge integration, they struggle with numerical time series due to inefficient text-based representations and limited exposure to temporal data during pretraining. We address this gap by augmenting an LLM with specialized time series perception through a patch-based encoder-decoder architecture. We train this Time Series-augmented LLM (TsLLM) on a large corpus of over 2 million interleaved time series and text examples spanning diverse analysis tasks: forecasting with contextual information, time series question-answering, pattern explanation, classification with natural language outputs, and report generation. This training enables TsLLM to leverage both its language understanding and newly acquired temporal reasoning capabilities. While not designed to surpass specialized models on traditional benchmarks, TsLLM demonstrates strong performance on tasks requiring the integration of time series analysis with natural language -- capabilities that existing approaches cannot provide. Our work establishes a new paradigm for time series analysis that bridges numerical computation and natural language understanding, democratizing access to sophisticated temporal reasoning through natural language interaction.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

The past decade has witnessed significant advances in time series modeling with deep learning. While achieving state-of-the-art results, the best-performing architectures vary highly across applications and domains. Meanwhile, for natural language processing, the Generative Pre-trained Transformer (GPT) has demonstrated impressive performance via training one general-purpose model across various textual datasets. It is intriguing to explore whether GPT-type architectures can be effective for time series, capturing the intrinsic dynamic attributes and leading to significant accuracy improvements. In this paper, we propose a novel framework, TEMPO, that can effectively learn time series representations. We focus on utilizing two essential inductive biases of the time series task for pre-trained models: (i) decomposition of the complex interaction between trend, seasonal and residual components; and (ii) introducing the selection-based prompts to facilitate distribution adaptation in non-stationary time series. TEMPO expands the capability for dynamically modeling real-world temporal phenomena from data within diverse domains. Our experiments demonstrate the superior performance of TEMPO over state-of-the-art methods on a number of time series benchmark datasets. This performance gain is observed not only in standard supervised learning settings but also in scenarios involving previously unseen datasets as well as in scenarios with multi-modal inputs. This compelling finding highlights TEMPO's potential to constitute a foundational model-building framework.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

Recent innovations in transformers have shown their superior performance in natural language processing (NLP) and computer vision (CV). The ability to capture long-range dependencies and interactions in sequential data has also triggered a great interest in time series modeling, leading to the widespread use of transformers in many time series applications. However, being the most common and crucial application, the adaptation of transformers to time series forecasting has remained limited, with both promising and inconsistent results. In contrast to the challenges in NLP and CV, time series problems not only add the complexity of order or temporal dependence among input sequences but also consider trend, level, and seasonality information that much of this data is valuable for decision making. The conventional training scheme has shown deficiencies regarding model overfitting, data scarcity, and privacy issues when working with transformers for a forecasting task. In this work, we propose attentive federated transformers for time series stock forecasting with better performance while preserving the privacy of participating enterprises. Empirical results on various stock data from the Yahoo! Finance website indicate the superiority of our proposed scheme in dealing with the above challenges and data heterogeneity in federated learning.

Transformer-based models have significantly advanced time series forecasting, with patch-based input strategies offering efficiency and improved long-horizon modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and fixed lengths fracture temporal coherence by splitting natural transitions across boundaries. This naive segmentation often disrupts short-term dependencies and weakens representation learning. In response, we propose EntroPE (Entropy-Guided Dynamic Patch Encoder), a novel, temporally informed framework that dynamically detects transition points via conditional entropy and dynamically places patch boundaries. This preserves temporal structure while retaining the computational benefits of patching. EntroPE consists of two key modules, namely an Entropy-based Dynamic Patcher (EDP) that applies information-theoretic criteria to locate natural temporal shifts and determine patch boundaries, and an Adaptive Patch Encoder (APE) that employs pooling and cross-attention to capture intra-patch dependencies and produce fixed-size latent representations. These embeddings are then processed by a global transformer to model inter-patch dynamics. Experiments across long-term forecasting benchmarks demonstrate that EntroPE improves both accuracy and efficiency, establishing entropy-guided dynamic patching as a promising new paradigm for time series modeling. Code is available at: https://github.com/Sachithx/EntroPE.

Modern enterprises generate vast streams of time series metrics when monitoring complex systems, known as observability data. Unlike conventional time series from domains such as weather, observability data are zero-inflated, highly stochastic, and exhibit minimal temporal structure. Despite their importance, observability datasets are underrepresented in public benchmarks due to proprietary restrictions. Existing datasets are often anonymized and normalized, removing scale information and limiting their use for tasks beyond forecasting, such as anomaly detection, root-cause analysis, and multi-modal reasoning. To address this gap, we introduce TelecomTS, a large-scale observability dataset derived from a 5G telecommunications network. TelecomTS features heterogeneous, de-anonymized covariates with explicit scale information and supports a suite of downstream tasks, including anomaly detection, root-cause analysis, and a question-answering benchmark requiring multi-modal reasoning. Benchmarking state-of-the-art time series, language, and reasoning models reveals that existing approaches struggle with the abrupt, noisy, and high-variance dynamics of observability data. Our experiments also underscore the importance of preserving covariates' absolute scale, emphasizing the need for foundation time series models that natively leverage scale information for practical observability applications.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper explores further XNet, a novel algorithm that employs the complex-valued Cauchy integral formula, offering a superior network architecture that surpasses traditional Multi-Layer Perceptrons (MLPs) and Kolmogorov-Arnold Networks (KANs). XNet significant improves speed and accuracy across various tasks in both low and high-dimensional spaces, redefining the scope of data-driven model development and providing substantial improvements over established time series models like LSTMs.

In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets' risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts.

Financial markets pose fundamental challenges for asset return prediction due to their high dimensionality, non-stationarity, and persistent volatility. Despite advances in large language models and multi-agent systems, current quantitative research pipelines suffer from limited automation, weak interpretability, and fragmented coordination across key components such as factor mining and model innovation. In this paper, we propose R&D-Agent for Quantitative Finance, in short RD-Agent(Q), the first data-centric multi-agent framework designed to automate the full-stack research and development of quantitative strategies via coordinated factor-model co-optimization. RD-Agent(Q) decomposes the quant process into two iterative stages: a Research stage that dynamically sets goal-aligned prompts, formulates hypotheses based on domain priors, and maps them to concrete tasks, and a Development stage that employs a code-generation agent, Co-STEER, to implement task-specific code, which is then executed in real-market backtests. The two stages are connected through a feedback stage that thoroughly evaluates experimental outcomes and informs subsequent iterations, with a multi-armed bandit scheduler for adaptive direction selection. Empirically, RD-Agent(Q) achieves up to 2X higher annualized returns than classical factor libraries using 70% fewer factors, and outperforms state-of-the-art deep time-series models on real markets. Its joint factor-model optimization delivers a strong balance between predictive accuracy and strategy robustness. Our code is available at: https://github.com/microsoft/RD-Agent.

Pretrained time series models have enabled inference-only forecasting systems that produce accurate predictions without task-specific training. However, existing approaches largely focus on univariate forecasting, limiting their applicability in real-world scenarios where multivariate data and covariates play a crucial role. We present Chronos-2, a pretrained model capable of handling univariate, multivariate, and covariate-informed forecasting tasks in a zero-shot manner. Chronos-2 employs a group attention mechanism that facilitates in-context learning (ICL) through efficient information sharing across multiple time series within a group, which may represent sets of related series, variates of a multivariate series, or targets and covariates in a forecasting task. These general capabilities are achieved through training on synthetic datasets that impose diverse multivariate structures on univariate series. Chronos-2 delivers state-of-the-art performance across three comprehensive benchmarks: fev-bench, GIFT-Eval, and Chronos Benchmark II. On fev-bench, which emphasizes multivariate and covariate-informed forecasting, Chronos-2's universal ICL capabilities lead to substantial improvements over existing models. On tasks involving covariates, it consistently outperforms baselines by a wide margin. Case studies in the energy and retail domains further highlight its practical advantages. The in-context learning capabilities of Chronos-2 establish it as a general-purpose forecasting model that can be used "as is" in real-world forecasting pipelines.

Developing professional, structured reasoning on par with human financial analysts and traders remains a central challenge in AI for finance, where markets demand interpretability and trust. Traditional time-series models lack explainability, while LLMs face challenges in turning natural-language analysis into disciplined, executable trades. Although reasoning LLMs have advanced in step-by-step planning and verification, their application to risk-sensitive financial decisions is underexplored. We present Trading-R1, a financially-aware model that incorporates strategic thinking and planning for comprehensive thesis composition, facts-grounded analysis, and volatility-adjusted decision making. Trading-R1 aligns reasoning with trading principles through supervised fine-tuning and reinforcement learning with a three-stage easy-to-hard curriculum. Training uses Tauric-TR1-DB, a 100k-sample corpus spanning 18 months, 14 equities, and five heterogeneous financial data sources. Evaluated on six major equities and ETFs, Trading-R1 demonstrates improved risk-adjusted returns and lower drawdowns compared to both open-source and proprietary instruction-following models as well as reasoning models. The system generates structured, evidence-based investment theses that support disciplined and interpretable trading decisions. Trading-R1 Terminal will be released at https://github.com/TauricResearch/Trading-R1.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.

Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL) and time-series prediction. A significant advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically tailored for memory-intensive tasks encompassing partially observable environments and non-linear time-series prediction. Nevertheless, QRNN-based models encounter challenges, notably prolonged training duration stemming from the necessity to compute quantum gradients using backpropagation-through-time (BPTT). This predicament exacerbates when executing the complete model on quantum devices, primarily due to the substantial demand for circuit evaluation arising from the parameter-shift rule. This paper introduces the Quantum Fast Weight Programmers (QFWP) as a solution to the temporal or sequential learning challenge. The QFWP leverages a classical neural network (referred to as the 'slow programmer') functioning as a quantum programmer to swiftly modify the parameters of a variational quantum circuit (termed the 'fast programmer'). Instead of completely overwriting the fast programmer at each time-step, the slow programmer generates parameter changes or updates for the quantum circuit parameters. This approach enables the fast programmer to incorporate past observations or information. Notably, the proposed QFWP model achieves learning of temporal dependencies without necessitating the use of quantum recurrent neural networks. Numerical simulations conducted in this study showcase the efficacy of the proposed QFWP model in both time-series prediction and RL tasks. The model exhibits performance levels either comparable to or surpassing those achieved by QLSTM-based models.

Predicting stock market movements has always been of great interest to investors and an active area of research. Research has proven that popularity of products is highly influenced by what people talk about. Social media like Twitter, Reddit have become hotspots of such influences. This paper investigates the impact of social media posts on close price prediction of stocks using Twitter and Reddit posts. Our objective is to integrate sentiment of social media data with historical stock data and study its effect on closing prices using time series models. We carried out rigorous experiments and deep analysis using multiple deep learning based models on different datasets to study the influence of posts by executives and general people on the close price. Experimental results on multiple stocks (Apple and Tesla) and decentralised currencies (Bitcoin and Ethereum) consistently show improvements in prediction on including social media data and greater improvements on including executive posts.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Time series foundation models (TSFMs) offer strong zero-shot forecasting via large-scale pre-training, yet fine-tuning remains critical for boosting performance in domains with limited public data. With the growing number of TSFMs, efficiently identifying the best model for downstream fine-tuning becomes increasingly challenging. In this work, we introduce TimeTic, a transferability estimation framework that recasts model selection as an in-context-learning problem: given observations on known (source) datasets, it predicts how a TSFM will perform after fine-tuning on a downstream (target) dataset. TimeTic flexibly organizes the observed model-data relationships as contextual information, allowing it to adapt seamlessly to various test-time scenarios. Leveraging the natural tabular structure formed by dataset meta-features, model characteristics, and fine-tuned performance, we employ tabular foundation models to serve as in-context learners. We further introduce a novel model characterization based on entropy evolution across model layers, capturing embedding-space distinctions and enabling TimeTic to generalize across arbitrary model sets. We establish a comprehensive benchmark for transferability estimation including 10 datasets, 10 foundation models, and 3 forecasting tasks. On this benchmark, TimeTic's estimation demonstrates strong alignment with actual fine-tuned performance for previously unseen datasets, achieving a mean rank correlation of approximately 0.6 and a 30% improvement compared to using zero-shot performance as the transferability score.

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General Time Series Forecasting Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 28 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The codebase, datasets, and a leaderboard showing all the results in detail will be available soon.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

In this paper, we investigate the distillation of time series reasoning capabilities into small, instruction-tuned language models as a step toward building interpretable time series foundation models. Leveraging a synthetic dataset of mean-reverting time series with systematically varied trends and noise levels, we generate natural language annotations using a large multimodal model and use these to supervise the fine-tuning of compact Qwen models. We introduce evaluation metrics that assess the quality of the distilled reasoning - focusing on trend direction, noise intensity, and extremum localization - and show that the post-trained models acquire meaningful interpretive capabilities. Our results highlight the feasibility of compressing time series understanding into lightweight, language-capable models suitable for on-device or privacy-sensitive deployment. This work contributes a concrete foundation toward developing small, interpretable models that explain temporal patterns in natural language.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

Energy markets exhibit complex causal relationships between weather patterns, generation technologies, and price formation, with regime changes occurring continuously rather than at discrete break points. Current approaches model electricity prices without explicit causal interpretation or counterfactual reasoning capabilities. We introduce Augmented Time Series Causal Models (ATSCM) for energy markets, extending counterfactual reasoning frameworks to multivariate temporal data with learned causal structure. Our approach models energy systems through interpretable factors (weather, generation mix, demand patterns), rich grid dynamics, and observable market variables. We integrate neural causal discovery to learn time-varying causal graphs without requiring ground truth DAGs. Applied to real-world electricity price data, ATSCM enables novel counterfactual queries such as "What would prices be under different renewable generation scenarios?".

We introduce Toto, a time series forecasting foundation model with 151 million parameters. Toto uses a modern decoder-only architecture coupled with architectural innovations designed to account for specific challenges found in multivariate observability time series data. Toto's pre-training corpus is a mixture of observability data, open datasets, and synthetic data, and is 4-10times larger than those of leading time series foundation models. Additionally, we introduce BOOM, a large-scale benchmark consisting of 350 million observations across 2,807 real-world time series. For both Toto and BOOM, we source observability data exclusively from Datadog's own telemetry and internal observability metrics. Extensive evaluations demonstrate that Toto achieves state-of-the-art performance on both BOOM and on established general purpose time series forecasting benchmarks. Toto's model weights, inference code, and evaluation scripts, as well as BOOM's data and evaluation code, are all available as open source under the Apache 2.0 License available at https://huggingface.co/Datadog/Toto-Open-Base-1.0 and https://github.com/DataDog/toto.

Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pre-training. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverages historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot settings with much better efficiency compared with existing time series foundation models.

We introduce EarthPT -- an Earth Observation (EO) pretrained transformer. EarthPT is a 700 million parameter decoding transformer foundation model trained in an autoregressive self-supervised manner and developed specifically with EO use-cases in mind. We demonstrate that EarthPT is an effective forecaster that can accurately predict future pixel-level surface reflectances across the 400-2300 nm range well into the future. For example, forecasts of the evolution of the Normalised Difference Vegetation Index (NDVI) have a typical error of approximately 0.05 (over a natural range of -1 -> 1) at the pixel level over a five month test set horizon, out-performing simple phase-folded models based on historical averaging. We also demonstrate that embeddings learnt by EarthPT hold semantically meaningful information and could be exploited for downstream tasks such as highly granular, dynamic land use classification. Excitingly, we note that the abundance of EO data provides us with -- in theory -- quadrillions of training tokens. Therefore, if we assume that EarthPT follows neural scaling laws akin to those derived for Large Language Models (LLMs), there is currently no data-imposed limit to scaling EarthPT and other similar `Large Observation Models.'

Recent studies have indicated that vision models pre-trained on images can serve as time series foundation models (TSFMs) by reformulating time series forecasting (TSF) as image reconstruction. However, effective cross-modal transfer from vision to time series remains challenging due to three discrepancies: (1) the data-modality gap between structured, bounded image data and unbounded, heterogeneous time series; (2) the multivariate-forecasting gap between fixed RGB-three-channel vision models and time series with arbitrary numbers of variates; and (3) the probabilistic-forecasting gap between the deterministic outputs of vision models and the requirement for uncertainty-aware probabilistic predictions. To bridge these gaps, we propose VisonTS++, a TSFM based on continual pre-training of a vision model on large-scale time series. Our approach introduces three key innovations: (1) vision-model-based filtering to identify high-quality sequences to stabilize pre-training and mitigate modality gap; (2) colorized multivariate conversion, encoding multivariate series as multi-subfigure RGB images to enhance cross-variate modeling; (3) multi-quantile forecasting, using parallel reconstruction heads to generate quantile forecasts without parametric assumptions. Experiments show that VisionTS++ achieves state-of-the-art performance in both in-distribution and out-of-distribution forecasting, outperforming specialized TSFMs by 6%-44% in MSE reduction and ranking first in GIFT-Eval benchmark which comprises 23 datasets across 7 domains. Our work demonstrates that with appropriate adaptation, vision models can effectively generalize to TSF, thus advancing the pursuit of universal TSFMs. Code is available at https://github.com/HALF111/VisionTSpp.

Human experts typically integrate numerical and textual multimodal information to analyze time series. However, most traditional deep learning predictors rely solely on unimodal numerical data, using a fixed-length window for training and prediction on a single dataset, and cannot adapt to different scenarios. The powered pre-trained large language model has introduced new opportunities for time series analysis. Yet, existing methods are either inefficient in training, incapable of handling textual information, or lack zero-shot forecasting capability. In this paper, we innovatively model time series as a foreign language and construct ChatTime, a unified framework for time series and text processing. As an out-of-the-box multimodal time series foundation model, ChatTime provides zero-shot forecasting capability and supports bimodal input/output for both time series and text. We design a series of experiments to verify the superior performance of ChatTime across multiple tasks and scenarios, and create four multimodal datasets to address data gaps. The experimental results demonstrate the potential and utility of ChatTime.

AI systems are notorious for their fragility; minor input changes can potentially cause major output swings. When such systems are deployed in critical areas like finance, the consequences of their uncertain behavior could be severe. In this paper, we focus on multi-modal time-series forecasting, where imprecision due to noisy or incorrect data can lead to erroneous predictions, impacting stakeholders such as analysts, investors, and traders. Recently, it has been shown that beyond numeric data, graphical transformations can be used with advanced visual models to achieve better performance. In this context, we introduce a rating methodology to assess the robustness of Multi-Modal Time-Series Forecasting Models (MM-TSFM) through causal analysis, which helps us understand and quantify the isolated impact of various attributes on the forecasting accuracy of MM-TSFM. We apply our novel rating method on a variety of numeric and multi-modal forecasting models in a large experimental setup (six input settings of control and perturbations, ten data distributions, time series from six leading stocks in three industries over a year of data, and five time-series forecasters) to draw insights on robust forecasting models and the context of their strengths. Within the scope of our study, our main result is that multi-modal (numeric + visual) forecasting, which was found to be more accurate than numeric forecasting in previous studies, can also be more robust in diverse settings. Our work will help different stakeholders of time-series forecasting understand the models` behaviors along trust (robustness) and accuracy dimensions to select an appropriate model for forecasting using our rating method, leading to improved decision-making.

Developing models and algorithms to predict nonstationary time series is a long standing statistical problem. It is crucial for many applications, in particular for fashion or retail industries, to make optimal inventory decisions and avoid massive wastes. By tracking thousands of fashion trends on social media with state-of-the-art computer vision approaches, we propose a new model for fashion time series forecasting. Our contribution is twofold. We first provide publicly a dataset gathering 10000 weekly fashion time series. As influence dynamics are the key of emerging trend detection, we associate with each time series an external weak signal representing behaviours of influencers. Secondly, to leverage such a dataset, we propose a new hybrid forecasting model. Our approach combines per-time-series parametric models with seasonal components and a global recurrent neural network to include sporadic external signals. This hybrid model provides state-of-the-art results on the proposed fashion dataset, on the weekly time series of the M4 competition, and illustrates the benefit of the contribution of external weak signals.

Large pre-trained time series foundation models (TSFMs) have demonstrated promising zero-shot performance across a wide range of domains. However, a question remains: Do TSFMs succeed solely by memorizing training patterns, or do they possess the ability to reason? While reasoning is a topic of great interest in the study of Large Language Models (LLMs), it is undefined and largely unexplored in the context of TSFMs. In this work, inspired by language modeling literature, we formally define compositional reasoning in forecasting and distinguish it from in-distribution generalization. We evaluate the reasoning and generalization capabilities of 23 popular deep learning forecasting models on multiple synthetic and real-world datasets. Additionally, through controlled studies, we systematically examine which design choices in TSFMs contribute to improved reasoning abilities. Our study yields key insights into the impact of TSFM architecture design on compositional reasoning and generalization. We find that patch-based Transformers have the best reasoning performance, closely followed by residualized MLP-based architectures, which are 97\% less computationally complex in terms of FLOPs and 86\% smaller in terms of the number of trainable parameters. Interestingly, in some zero-shot out-of-distribution scenarios, these models can outperform moving average and exponential smoothing statistical baselines trained on in-distribution data. Only a few design choices, such as the tokenization method, had a significant (negative) impact on Transformer model performance.

Recent advances in deep learning have driven rapid progress in time series forecasting, yet many state-of-the-art models continue to struggle with robust performance in real-world applications, even when they achieve strong results on standard benchmark datasets. This persistent gap can be attributed to the black-box nature of deep learning architectures and the inherent limitations of current evaluation frameworks, which frequently lack the capacity to provide clear, quantitative insights into the specific strengths and weaknesses of different models, thereby complicating the selection of appropriate models for particular forecasting scenarios. To address these issues, we propose a synthetic data-driven evaluation paradigm, SynTSBench, that systematically assesses fundamental modeling capabilities of time series forecasting models through programmable feature configuration. Our framework isolates confounding factors and establishes an interpretable evaluation system with three core analytical dimensions: (1) temporal feature decomposition and capability mapping, which enables systematic evaluation of model capacities to learn specific pattern types; (2) robustness analysis under data irregularities, which quantifies noise tolerance thresholds and anomaly recovery capabilities; and (3) theoretical optimum benchmarking, which establishes performance boundaries for each pattern type-enabling direct comparison between model predictions and mathematical optima. Our experiments show that current deep learning models do not universally approach optimal baselines across all types of temporal features.The code is available at https://github.com/TanQitai/SynTSBench

This paper presents OLinear, a linear-based multivariate time series forecasting model that operates in an orthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we utilize OrthoTrans, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix. This approach enables more effective encoding and decoding in the decorrelated feature domain and can serve as a plug-in module to enhance existing forecasters. To enhance the representation learning for multivariate time series, we introduce a customized linear layer, NormLin, which employs a normalized weight matrix to capture multivariate dependencies. Empirically, the NormLin module shows a surprising performance advantage over multi-head self-attention, while requiring nearly half the FLOPs. Extensive experiments on 24 benchmarks and 140 forecasting tasks demonstrate that OLinear consistently achieves state-of-the-art performance with high efficiency. Notably, as a plug-in replacement for self-attention, the NormLin module consistently enhances Transformer-based forecasters. The code and datasets are available at https://anonymous.4open.science/r/OLinear

We present TimeFound, an encoder-decoder transformer-based time series foundation model for out-of-the-box zero-shot forecasting. To handle time series data from various domains, TimeFound employs a multi-resolution patching strategy to capture complex temporal patterns at multiple scales. We pre-train our model with two sizes (200M and 710M parameters) on a large time-series corpus comprising both real-world and synthetic datasets. Over a collection of unseen datasets across diverse domains and forecasting horizons, our empirical evaluations suggest that TimeFound can achieve superior or competitive zero-shot forecasting performance, compared to state-of-the-art time series foundation models.

Foundation models have become increasingly popular for forecasting due to their ability to provide predictions without requiring a lot of training data. In this work, we demonstrate how TabPFN-v2, a general tabular foundation model, can be effectively applied to time series forecasting. We introduce TabPFN-TS, a simple method that combines TabPFN-v2 with lightweight feature engineering to enable both point and probabilistic forecasting. Despite its simplicity and compact size (11M parameters), TabPFN-TS achieves top rank on the public GIFT-Eval leaderboard in both forecasting tasks. Through ablation studies, we investigate factors contributing to this surprising effectiveness, especially considering TabPFN-v2 was pretrained solely on synthetic tabular data with no exposure to time series. Our results highlights the potential of tabular foundation models like TabPFN-v2 as a valuable new approach for time series forecasting. Our implementation is available at https://github.com/PriorLabs/tabpfn-time-series.

The advent of universal time series forecasting models has revolutionized zero-shot forecasting across diverse domains, yet the critical role of data diversity in training these models remains underexplored. Existing large-scale time series datasets often suffer from inherent biases and imbalanced distributions, leading to suboptimal model performance and generalization. To address this gap, we introduce BLAST, a novel pre-training corpus designed to enhance data diversity through a balanced sampling strategy. First, BLAST incorporates 321 billion observations from publicly available datasets and employs a comprehensive suite of statistical metrics to characterize time series patterns. Then, to facilitate pattern-oriented sampling, the data is implicitly clustered using grid-based partitioning. Furthermore, by integrating grid sampling and grid mixup techniques, BLAST ensures a balanced and representative coverage of diverse patterns. Experimental results demonstrate that models pre-trained on BLAST achieve state-of-the-art performance with a fraction of the computational resources and training tokens required by existing methods. Our findings highlight the pivotal role of data diversity in improving both training efficiency and model performance for the universal forecasting task.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

Transformers have gained popularity in time series forecasting for their ability to capture long-sequence interactions. However, their high memory and computing requirements pose a critical bottleneck for long-term forecasting. To address this, we propose TSMixer, a lightweight neural architecture exclusively composed of multi-layer perceptron (MLP) modules for multivariate forecasting and representation learning on patched time series. Inspired by MLP-Mixer's success in computer vision, we adapt it for time series, addressing challenges and introducing validated components for enhanced accuracy. This includes a novel design paradigm of attaching online reconciliation heads to the MLP-Mixer backbone, for explicitly modeling the time-series properties such as hierarchy and channel-correlations. We also propose a novel Hybrid channel modeling and infusion of a simple gating approach to effectively handle noisy channel interactions and generalization across diverse datasets. By incorporating these lightweight components, we significantly enhance the learning capability of simple MLP structures, outperforming complex Transformer models with minimal computing usage. Moreover, TSMixer's modular design enables compatibility with both supervised and masked self-supervised learning methods, making it a promising building block for time-series Foundation Models. TSMixer outperforms state-of-the-art MLP and Transformer models in forecasting by a considerable margin of 8-60%. It also outperforms the latest strong benchmarks of Patch-Transformer models (by 1-2%) with a significant reduction in memory and runtime (2-3X). The source code of our model is officially released as PatchTSMixer in the HuggingFace. Model: https://huggingface.co/docs/transformers/main/en/model_doc/patchtsmixer Examples: https://github.com/ibm/tsfm/#notebooks-links

Time series forecasting plays a crucial role in data mining, driving rapid advancements across numerous industries. With the emergence of large models, time series foundation models (TSFMs) have exhibited remarkable generalization capabilities, such as zero-shot learning, through large-scale pre-training. Meanwhile, Retrieval-Augmented Generation (RAG) methods have been widely employed to enhance the performance of foundation models on unseen data, allowing models to access to external knowledge. In this paper, we introduce TimeRAF, a Retrieval-Augmented Forecasting model that enhance zero-shot time series forecasting through retrieval-augmented techniques. We develop customized time series knowledge bases that are tailored to the specific forecasting tasks. TimeRAF employs an end-to-end learnable retriever to extract valuable information from the knowledge base. Additionally, we propose Channel Prompting for knowledge integration, which effectively extracts relevant information from the retrieved knowledge along the channel dimension. Extensive experiments demonstrate the effectiveness of our model, showing significant improvement across various domains and datasets.

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper, we propose TimeDiff, a non-autoregressive diffusion model that achieves high-quality time series prediction with the introduction of two novel conditioning mechanisms: future mixup and autoregressive initialization. Similar to teacher forcing, future mixup allows parts of the ground-truth future predictions for conditioning, while autoregressive initialization helps better initialize the model with basic time series patterns such as short-term trends. Extensive experiments are performed on nine real-world datasets. Results show that TimeDiff consistently outperforms existing time series diffusion models, and also achieves the best overall performance across a variety of the existing strong baselines (including transformers and FiLM).

We present a joint forecasting framework for time series prediction that contrasts with traditional direct or recursive methods. This framework achieves state-of-the-art performance for our designed foundation model, YingLong, and reveals a novel scaling effect: longer outputs significantly enhance model accuracy due to delayed chain-of-thought reasoning in our non-causal approach. YingLong is a non-causal, bidirectional attention encoder-only transformer trained through masked token recovery, aligning more effectively with language understanding tasks than with generation tasks. Additionally, we boost performance by tackling output variance with a multi-input ensemble. We release four foundation models ranging from 6M to 300M parameters, demonstrating superior results in zero-shot tasks on the ETT and Weather datasets. YingLong achieves more than 60% best performance. To ensure generalizability, we assessed the models using the GIFT-Eval benchmark, which comprises 23 time series datasets across 7 domains. Yinglong significantly outperformed the best time-series foundation models, end-to-end trained models by 14% and 44% in rank respectively.The pretrained 300M model is available at https://huggingface.co/qcw1314/YingLong_300m

Time series anomaly detection forms a very crucial area in several domains but poses substantial challenges. Due to time series data possessing seasonality, trends, noise, and evolving patterns (concept drift), it becomes very difficult to set a general notion of what constitutes normal behavior. Anomalies themselves could be varied, ranging from a single outlier to contextual or collective anomalies, and are normally very rare; hence, the dataset is largely imbalanced. Additional layers of complexities arise due to the problems of increased dimensionality of modern time series, real-time detection criteria, setting up appropriate detection thresholds, and arriving at results that are interpretable. To embrace these multifaceted challenges, very strong, flexible, and interpretable approaches are required. This paper presents THEMIS, a new framework for time series anomaly detection that exploits pretrained knowledge from foundation models. THEMIS extracts embeddings from the encoder of the Chronos time series foundation model and applies outlier detection techniques like Local Outlier Factor and Spectral Decomposition on the self-similarity matrix, to spot anomalies in the data. Our experiments show that this modular method achieves SOTA results on the MSL dataset and performs quite competitively on the SMAP and SWAT^* datasets. Notably, THEMIS exceeds models trained specifically for anomaly detection, presenting hyperparameter robustness and interpretability by default. This paper advocates for pretrained representations from foundation models for performing efficient and adaptable anomaly detection for time series data.

Recent research has demonstrated the potential of deep neural networks (DNNs) to accurately predict wildfire spread on a given day based upon high-dimensional explanatory data from a single preceding day, or from a time series of T preceding days. For the first time, we investigate a large number of existing data-driven wildfire modeling strategies under controlled conditions, revealing the best modeling strategies and resulting in models that achieve state-of-the-art (SOTA) accuracy for both single-day and multi-day input scenarios, as evaluated on a large public benchmark for next-day wildfire spread, termed the WildfireSpreadTS (WSTS) benchmark. Consistent with prior work, we found that models using time-series input obtained the best overall accuracy, suggesting this is an important future area of research. Furthermore, we create a new benchmark, WSTS+, by incorporating four additional years of historical wildfire data into the WSTS benchmark. Our benchmark doubles the number of unique years of historical data, expands its geographic scope, and, to our knowledge, represents the largest public benchmark for time-series-based wildfire spread prediction.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

Interpretable time series prediction is crucial for safety-critical areas such as healthcare and autonomous driving. Most existing methods focus on interpreting predictions by assigning important scores to segments of time series. In this paper, we take a different and more challenging route and aim at developing a self-interpretable model, dubbed Counterfactual Time Series (CounTS), which generates counterfactual and actionable explanations for time series predictions. Specifically, we formalize the problem of time series counterfactual explanations, establish associated evaluation protocols, and propose a variational Bayesian deep learning model equipped with counterfactual inference capability of time series abduction, action, and prediction. Compared with state-of-the-art baselines, our self-interpretable model can generate better counterfactual explanations while maintaining comparable prediction accuracy.

Time series classification is a fundamental task in healthcare and industry, yet the development of time series foundation models (TSFMs) remains limited by the scarcity of publicly available time series datasets. In this work, we propose Time Vision Transformer (TiViT), a framework that converts time series into images to leverage the representational power of frozen Vision Transformers (ViTs) pretrained on large-scale image datasets. First, we theoretically motivate our approach by analyzing the 2D patching of ViTs for time series, showing that it can increase the number of label-relevant tokens and reduce the sample complexity. Second, we empirically demonstrate that TiViT achieves state-of-the-art performance on standard time series classification benchmarks by utilizing the hidden representations of large OpenCLIP models. We explore the structure of TiViT representations and find that intermediate layers with high intrinsic dimension are the most effective for time series classification. Finally, we assess the alignment between TiViT and TSFM representation spaces and identify a strong complementarity, with further performance gains achieved by combining their features. Our findings reveal a new direction for reusing vision representations in a non-visual domain. Code is available at https://github.com/ExplainableML/TiViT.

Time series forecasting is a foundational task across domains, such as finance, healthcare, and environmental monitoring. While recent advances in Time Series Foundation Models (TSFMs) have demonstrated strong generalisation through large-scale pretraining, existing models operate predominantly in a unimodal setting, ignoring the rich multimodal context, such as visual and textual signals, that often accompanies time series data in real-world scenarios. This paper introduces a novel parameter-efficient multimodal framework, UniCast, that extends TSFMs to jointly leverage time series, vision, and text modalities for enhanced forecasting performance. Our method integrates modality-specific embeddings from pretrained Vision and Text Encoders with a frozen TSFM via soft prompt tuning, enabling efficient adaptation with minimal parameter updates. This design not only preserves the generalisation strength of the foundation model but also enables effective cross-modal interaction. Extensive experiments across diverse time-series forecasting benchmarks demonstrate that UniCast consistently and significantly outperforms all existing TSFM baselines. The findings highlight the critical role of multimodal context in advancing the next generation of general-purpose time series forecasters.

This technical report describes the Time Series Optimized Transformer for Observability (Toto), a new state of the art foundation model for time series forecasting developed by Datadog. In addition to advancing the state of the art on generalized time series benchmarks in domains such as electricity and weather, this model is the first general-purpose time series forecasting foundation model to be specifically tuned for observability metrics. Toto was trained on a dataset of one trillion time series data points, the largest among all currently published time series foundation models. Alongside publicly available time series datasets, 75% of the data used to train Toto consists of fully anonymous numerical metric data points from the Datadog platform. In our experiments, Toto outperforms existing time series foundation models on observability data. It does this while also excelling at general-purpose forecasting tasks, achieving state-of-the-art zero-shot performance on multiple open benchmark datasets.

Recently, deep learning has driven significant advancements in multivariate time series forecasting (MTSF) tasks. However, much of the current research in MTSF tends to evaluate models from a holistic perspective, which obscures the individual contributions and leaves critical issues unaddressed. Adhering to the current modeling paradigms, this work bridges these gaps by systematically decomposing deep MTSF methods into their core, fine-grained components like series-patching tokenization, channel-independent strategy, attention modules, or even Large Language Models and Time-series Foundation Models. Through extensive experiments and component-level analysis, our work offers more profound insights than previous benchmarks that typically discuss models as a whole. Furthermore, we propose a novel automated solution called TSGym for MTSF tasks. Unlike traditional hyperparameter tuning, neural architecture searching or fixed model selection, TSGym performs fine-grained component selection and automated model construction, which enables the creation of more effective solutions tailored to diverse time series data, therefore enhancing model transferability across different data sources and robustness against distribution shifts. Extensive experiments indicate that TSGym significantly outperforms existing state-of-the-art MTSF and AutoML methods. All code is publicly available on https://github.com/SUFE-AILAB/TSGym.

Recent efforts have been dedicated to enhancing time series forecasting accuracy by introducing advanced network architectures and self-supervised pretraining strategies. Nevertheless, existing approaches still exhibit two critical drawbacks. Firstly, these methods often rely on a single dataset for training, limiting the model's generalizability due to the restricted scale of the training data. Secondly, the one-step generation schema is widely followed, which necessitates a customized forecasting head and overlooks the temporal dependencies in the output series, and also leads to increased training costs under different horizon length settings. To address these issues, we propose a novel generative pretrained hierarchical transformer architecture for forecasting, named GPHT. There are two aspects of key designs in GPHT. On the one hand, we advocate for constructing a mixed dataset for pretraining our model, comprising various datasets from diverse data scenarios. This approach significantly expands the scale of training data, allowing our model to uncover commonalities in time series data and facilitating improved transfer to specific datasets. On the other hand, GPHT employs an auto-regressive forecasting approach under the channel-independent assumption, effectively modeling temporal dependencies in the output series. Importantly, no customized forecasting head is required, enabling a single model to forecast at arbitrary horizon settings. We conduct sufficient experiments on eight datasets with mainstream self-supervised pretraining models and supervised models. The results demonstrated that GPHT surpasses the baseline models across various fine-tuning and zero/few-shot learning settings in the traditional long-term forecasting task, providing support for verifying the feasibility of pretrained time series large models.

Sequence and channel mixers, the core mechanism in sequence models, have become the de facto standard in time series analysis (TSA). However, recent studies have questioned the necessity of complex sequence mixers, such as attention mechanisms, demonstrating that simpler architectures can achieve comparable or even superior performance. This suggests that the benefits attributed to complex sequencemixers might instead emerge from other architectural or optimization factors. Based on this observation, we pose a central question: Are common sequence mixers necessary for time-series analysis? Therefore, we propose JustDense, an empirical study that systematically replaces sequence mixers in various well-established TSA models with dense layers. Grounded in the MatrixMixer framework, JustDense treats any sequence mixer as a mixing matrix and replaces it with a dense layer. This substitution isolates the mixing operation, enabling a clear theoretical foundation for understanding its role. Therefore, we conducted extensive experiments on 29 benchmarks covering five representative TSA tasks using seven state-of-the-art TSA models to address our research question. The results show that replacing sequence mixers with dense layers yields comparable or even superior performance. In the cases where dedicated sequence mixers still offer benefits, JustDense challenges the assumption that "deeper and more complex architectures are inherently better" in TSA.

Multivariable time series forecasting methods can integrate information from exogenous variables, leading to significant prediction accuracy gains. Transformer architecture has been widely applied in various time series forecasting models due to its ability to capture long-range sequential dependencies. However, a na\"ive application of transformers often struggles to effectively model complex relationships among variables over time. To mitigate against this, we propose a novel architecture, namely the Spectral Operator Neural Network (Sonnet). Sonnet applies learnable wavelet transformations to the input and incorporates spectral analysis using the Koopman operator. Its predictive skill relies on the Multivariable Coherence Attention (MVCA), an operation that leverages spectral coherence to model variable dependencies. Our empirical analysis shows that Sonnet yields the best performance on 34 out of 47 forecasting tasks with an average mean absolute error (MAE) reduction of 1.1% against the most competitive baseline (different per task). We further show that MVCA -- when put in place of the na\"ive attention used in various deep learning models -- can remedy its deficiencies, reducing MAE by 10.7% on average in the most challenging forecasting tasks.

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Foundation models for zero-shot time series forecasting face challenges in efficient long-horizon prediction and reproducibility, with existing synthetic-only approaches underperforming on challenging benchmarks. This paper presents TempoPFN, a univariate time series foundation model based on linear Recurrent Neural Networks (RNNs) pre-trained exclusively on synthetic data. The model uses a GatedDeltaProduct architecture with state-weaving for fully parallelizable training across sequence lengths, eliminating the need for windowing or summarization techniques while maintaining robust temporal state-tracking. Our comprehensive synthetic data pipeline unifies diverse generators, including stochastic differential equations, Gaussian processes, and audio synthesis, with novel augmentations. In zero-shot evaluations on the Gift-Eval benchmark, TempoPFN achieves top-tier competitive performance, outperforming all existing synthetic-only approaches and surpassing the vast majority of models trained on real-world data, while being more efficient than existing baselines by leveraging fully parallelizable training and inference. We open-source our complete data generation pipeline and training code, providing a reproducible foundation for future research.

Recent works propose complex multi-modal models that handle both time series and language, ultimately claiming high performance on complex tasks like time series reasoning and cross-modal question-answering. However, they skip evaluations of simple and important foundational tasks, which complex models should reliably master. They also lack direct, head-to-head comparisons with other popular approaches. So we ask a simple question: Can recent models even produce generic visual descriptions of time series data? In response, we propose three new tasks, posing that successful multi-modal models should be able to recognize, differentiate, and generate language descriptions of time series. We then create BEDTime, the first benchmark dataset to assess models on each task, comprising four datasets reformatted for these tasks across multiple modalities. Using BEDTime, we evaluate 13 state-of-the-art models, and find that (1) surprisingly, dedicated time series foundation models severely underperform, despite being designed for similar tasks, (2) vision-language models are quite capable, (3) language-only methods perform worst, despite many lauding their potential, and (4) all approaches are clearly fragile to a range of realistic robustness tests, indicating avenues for future work.

The performance of time series forecasting has recently been greatly improved by the introduction of transformers. In this paper, we propose a general multi-scale framework that can be applied to the state-of-the-art transformer-based time series forecasting models (FEDformer, Autoformer, etc.). By iteratively refining a forecasted time series at multiple scales with shared weights, introducing architecture adaptations, and a specially-designed normalization scheme, we are able to achieve significant performance improvements, from 5.5% to 38.5% across datasets and transformer architectures, with minimal additional computational overhead. Via detailed ablation studies, we demonstrate the effectiveness of each of our contributions across the architecture and methodology. Furthermore, our experiments on various public datasets demonstrate that the proposed improvements outperform their corresponding baseline counterparts. Our code is publicly available in https://github.com/BorealisAI/scaleformer.

Pre-trained Large Language Models (LLMs) encapsulate large amounts of knowledge and take enormous amounts of compute to train. We make use of this resource, together with the observation that LLMs are able to transfer knowledge and performance from one domain or even modality to another seemingly-unrelated area, to help with multivariate demand time series forecasting. Attention in transformer-based methods requires something worth attending to -- more than just samples of a time-series. We explore different methods to map multivariate input time series into the LLM token embedding space. In particular, our novel multivariate patching strategy to embed time series features into decoder-only pre-trained Transformers produces results competitive with state-of-the-art time series forecasting models. We also use recently-developed weight-based diagnostics to validate our findings.

Multivariate Time Series (MTS) forecasting is a fundamental task with numerous real-world applications, such as transportation, climate, and epidemiology. While a myriad of powerful deep learning models have been developed for this task, few works have explored the robustness of MTS forecasting models to malicious attacks, which is crucial for their trustworthy employment in high-stake scenarios. To address this gap, we dive deep into the backdoor attacks on MTS forecasting models and propose an effective attack method named BackTime.By subtly injecting a few stealthy triggers into the MTS data, BackTime can alter the predictions of the forecasting model according to the attacker's intent. Specifically, BackTime first identifies vulnerable timestamps in the data for poisoning, and then adaptively synthesizes stealthy and effective triggers by solving a bi-level optimization problem with a GNN-based trigger generator. Extensive experiments across multiple datasets and state-of-the-art MTS forecasting models demonstrate the effectiveness, versatility, and stealthiness of attacks. The code is available at https://github.com/xiaolin-cs/BackTime.

Designing domain specific neural networks is a time-consuming, error-prone, and expensive task. Neural Architecture Search (NAS) exists to simplify domain-specific model development but there is a gap in the literature for time series classification on microcontrollers. Therefore, we adapt the concept of differentiable neural architecture search (DNAS) to solve the time-series classification problem on resource-constrained microcontrollers (MCUs). We introduce MicroNAS, a domain-specific HW-NAS system integration of DNAS, Latency Lookup Tables, dynamic convolutions and a novel search space specifically designed for time-series classification on MCUs. The resulting system is hardware-aware and can generate neural network architectures that satisfy user-defined limits on the execution latency and peak memory consumption. Our extensive studies on different MCUs and standard benchmark datasets demonstrate that MicroNAS finds MCU-tailored architectures that achieve performance (F1-score) near to state-of-the-art desktop models. We also show that our approach is superior in adhering to memory and latency constraints compared to domain-independent NAS baselines such as DARTS.

The maritime industry's continuous commitment to sustainability has led to a dedicated exploration of methods to reduce vessel fuel consumption. This paper undertakes this challenge through a machine learning approach, leveraging a real-world dataset spanning two years of a ferry in west coast Canada. Our focus centers on the creation of a time series forecasting model given the dynamic and static states, actions, and disturbances. This model is designed to predict dynamic states based on the actions provided, subsequently serving as an evaluative tool to assess the proficiency of the ferry's operation under the captain's guidance. Additionally, it lays the foundation for future optimization algorithms, providing valuable feedback on decision-making processes. To facilitate future studies, our code is available at https://github.com/pagand/model_optimze_vessel/tree/AAAI

The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis. Our pre-trained model is publicly available at https://github.com/shiyu-coder/Kronos.

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

Time series foundation models (TSFMs) pretrained on data from multiple domains have shown strong performance on diverse modeling tasks. Various efforts have been made to develop foundation models specific to electroencephalography (EEG) data, which records brain electrical activity as time series. However, no comparative analysis of EEG-specific foundation models (EEGFMs) versus general TSFMs has been performed on EEG-specific tasks. We introduce a novel Spatial-Temporal Adapter with Multi-Head Pooling (STAMP), which leverages univariate embeddings produced by a general TSFM, implicitly models spatial-temporal characteristics of EEG data, and achieves performance comparable to state-of-the-art EEGFMs. A comprehensive analysis is performed on 8 benchmark datasets of clinical tasks using EEG for classification, along with ablation studies. Our proposed adapter is lightweight in trainable parameters and flexible in the inputs it can accommodate, supporting easy modeling of EEG data using TSFMs.

The Internet of Things is an example domain where data is perpetually generated in ever-increasing quantities, reflecting the proliferation of connected devices and the formation of continuous data streams over time. Consequently, the demand for ad-hoc, cost-effective machine learning solutions must adapt to this evolving data influx. This study tackles the task of offloading in small gateways, exacerbated by their dynamic availability over time. An approach leveraging CPU utilization metrics using online and continual machine learning techniques is proposed to predict gateway availability. These methods are compared to popular machine learning algorithms and a recent time-series foundation model, Lag-Llama, for fine-tuned and zero-shot setups. Their performance is benchmarked on a dataset of CPU utilization measurements over time from an IoT gateway and focuses on model metrics such as prediction errors, training and inference times, and memory consumption. Our primary objective is to study new efficient ways to predict CPU performance in IoT environments. Across various scenarios, our findings highlight that ensemble and online methods offer promising results for this task in terms of accuracy while maintaining a low resource footprint.

In recent years, microservices have gained widespread adoption in IT operations due to their scalability, maintenance, and flexibility. However, it becomes challenging for site reliability engineers (SREs) to pinpoint the root cause due to the complex relationships in microservices when facing system malfunctions. Previous research employed structured learning methods (e.g., PC-algorithm) to establish causal relationships and derive root causes from causal graphs. Nevertheless, they ignored the temporal order of time series data and failed to leverage the rich information inherent in the temporal relationships. For instance, in cases where there is a sudden spike in CPU utilization, it can lead to an increase in latency for other microservices. However, in this scenario, the anomaly in CPU utilization occurs before the latency increase, rather than simultaneously. As a result, the PC-algorithm fails to capture such characteristics. To address these challenges, we propose RUN, a novel approach for root cause analysis using neural Granger causal discovery with contrastive learning. RUN enhances the backbone encoder by integrating contextual information from time series, and leverages a time series forecasting model to conduct neural Granger causal discovery. In addition, RUN incorporates Pagerank with a personalization vector to efficiently recommend the top-k root causes. Extensive experiments conducted on the synthetic and real-world microservice-based datasets demonstrate that RUN noticeably outperforms the state-of-the-art root cause analysis methods. Moreover, we provide an analysis scenario for the sock-shop case to showcase the practicality and efficacy of RUN in microservice-based applications. Our code is publicly available at https://github.com/zmlin1998/RUN.

In this note we examine the autoregressive generalization of the FNet algorithm, in which self-attention layers from the standard Transformer architecture are substituted with a trivial sparse-uniformsampling procedure based on Fourier transforms. Using the Wikitext-103 benchmark, we demonstratethat FNetAR retains state-of-the-art performance (25.8 ppl) on the task of causal language modelingcompared to a Transformer-XL baseline (24.2 ppl) with only half the number self-attention layers,thus providing further evidence for the superfluity of deep neural networks with heavily compoundedattention mechanisms. The autoregressive Fourier transform could likely be used for parameterreduction on most Transformer-based time-series prediction models.

Forecasting is a critical task in decision-making across numerous domains. While historical numerical data provide a start, they fail to convey the complete context for reliable and accurate predictions. Human forecasters frequently rely on additional information, such as background knowledge and constraints, which can efficiently be communicated through natural language. However, in spite of recent progress with LLM-based forecasters, their ability to effectively integrate this textual information remains an open question. To address this, we introduce "Context is Key" (CiK), a time-series forecasting benchmark that pairs numerical data with diverse types of carefully crafted textual context, requiring models to integrate both modalities; crucially, every task in CiK requires understanding textual context to be solved successfully. We evaluate a range of approaches, including statistical models, time series foundation models, and LLM-based forecasters, and propose a simple yet effective LLM prompting method that outperforms all other tested methods on our benchmark. Our experiments highlight the importance of incorporating contextual information, demonstrate surprising performance when using LLM-based forecasting models, and also reveal some of their critical shortcomings. This benchmark aims to advance multimodal forecasting by promoting models that are both accurate and accessible to decision-makers with varied technical expertise. The benchmark can be visualized at https://servicenow.github.io/context-is-key-forecasting/v0/.

Self-supervised learning has seen great success recently in unsupervised representation learning, enabling breakthroughs in natural language and image processing. However, these methods often rely on autoregressive and masked modeling, which aim to reproduce masked information in the input, which can be vulnerable to the presence of noise or confounding variables. To address this problem, Joint-Embedding Predictive Architectures (JEPA) has been introduced with the aim to perform self-supervised learning in the latent space. To leverage these advancements in the domain of time series, we introduce Time Series JEPA (TS-JEPA), an architecture specifically adapted for time series representation learning. We validate TS-JEPA on both classification and forecasting, showing that it can match or surpass current state-of-the-art baselines on different standard datasets. Notably, our approach demonstrates a strong performance balance across diverse tasks, indicating its potential as a robust foundation for learning general representations. Thus, this work lays the groundwork for developing future time series foundation models based on Joint Embedding.

Electroencephalogram (EEG) signals have emerged as a promising modality for biometric identification. While previous studies have explored the use of imagined speech with semantically meaningful words for subject identification, most have relied on additional visual or auditory cues. In this study, we introduce a cueless EEG-based imagined speech paradigm, where subjects imagine the pronunciation of semantically meaningful words without any external cues. This innovative approach addresses the limitations of prior methods by requiring subjects to select and imagine words from a predefined list naturally. The dataset comprises over 4,350 trials from 11 subjects across five sessions. We assess a variety of classification methods, including traditional machine learning techniques such as Support Vector Machines (SVM) and XGBoost, as well as time-series foundation models and deep learning architectures specifically designed for EEG classification, such as EEG Conformer and Shallow ConvNet. A session-based hold-out validation strategy was employed to ensure reliable evaluation and prevent data leakage. Our results demonstrate outstanding classification accuracy, reaching 97.93%. These findings highlight the potential of cueless EEG paradigms for secure and reliable subject identification in real-world applications, such as brain-computer interfaces (BCIs).

In this paper, we present a new approach to time series forecasting. Time series data are prevalent in many scientific and engineering disciplines. Time series forecasting is a crucial task in modeling time series data, and is an important area of machine learning. In this work we developed a novel method that employs Transformer-based machine learning models to forecast time series data. This approach works by leveraging self-attention mechanisms to learn complex patterns and dynamics from time series data. Moreover, it is a generic framework and can be applied to univariate and multivariate time series data, as well as time series embeddings. Using influenza-like illness (ILI) forecasting as a case study, we show that the forecasting results produced by our approach are favorably comparable to the state-of-the-art.